Details

Time bar (total: 28.8s)

sample70.0ms

Algorithm
intervals
Results
23.0ms288×body80valid
8.0ms95×body80nan

simplify1.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01718
13618
28118
317718
444118
5257318
done500118

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize19.0ms

Local error

Found 4 expressions with local error:

3.6b
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.2b
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.3b
(/ (* M D) (* 2.0 d))
10.1b
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
35×add-sqr-sqrt
27×prod-exp
23×add-cbrt-cube
19×div-exp associate-*r*
17×add-cube-cbrt *-un-lft-identity
14×times-frac
12×associate-*l*
10×pow-exp
8×unswap-sqr
7×pow1 unpow-prod-down sqrt-prod cbrt-unprod
5×cbrt-undiv
4×sqrt-div add-log-exp
3×associate-*r/ div-inv sqr-pow
2×pow-to-exp flip3-- *-commutative flip--
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num associate-/r* associate-/l*
Counts
4 → 113
Calls
4 calls:
33.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
5.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
13.0ms
(/ (* M D) (* 2.0 d))
42.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.2s

Counts
4 → 12
Calls
4 calls:
627.0ms
(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
530.0ms
(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
35.0ms
(/ (* M D) (* 2.0 d))
958.0ms
(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.5s

Counts
125 → 125
Iterations

Useful iterations: 2 (427.0ms)

IterNodesCost
02362311
16202115
230821929
done50011929

prune563.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.7b

localize34.0ms

Local error

Found 4 expressions with local error:

3.6b
(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l)))))
4.2b
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
5.0b
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.3b
(/ (* M D) (* 2.0 d))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
146×add-exp-log
81×prod-exp
36×div-exp
30×add-cbrt-cube
20×add-sqr-sqrt pow-exp
19×associate-*r*
15×add-cube-cbrt *-un-lft-identity
11×cbrt-unprod
10×times-frac
9×pow1
8×rec-exp 1-exp
7×sqrt-prod
6×cbrt-undiv
4×pow-to-exp sqrt-div associate-*l* add-log-exp
3×associate-*r/
2×flip3-- pow-prod-down *-commutative flip-- div-inv unswap-sqr
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/r* un-div-inv associate-/l*
Counts
4 → 121
Calls
4 calls:
21.0ms
(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l)))))
5.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
54.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
39.0ms
(/ (* M D) (* 2.0 d))

series2.0s

Counts
4 → 12
Calls
4 calls:
531.0ms
(* w0 (sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l)))))
599.0ms
(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
860.0ms
(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
39.0ms
(/ (* M D) (* 2.0 d))

simplify2.5s

Counts
133 → 133
Iterations

Useful iterations: 2 (523.0ms)

IterNodesCost
02502657
17172322
238271917
done50001917

prune543.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.2b

localize29.0ms

Local error

Found 4 expressions with local error:

3.6b
(* (pow (/ M (/ (* 2.0 d) D)) 2.0) h)
3.6b
(* w0 (sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l)))))
4.2b
(sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l))))
5.0b
(* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
130×add-exp-log
64×prod-exp
44×add-sqr-sqrt
40×times-frac
39×div-exp
34×associate-*l*
31×add-cube-cbrt *-un-lft-identity
28×unpow-prod-down
22×associate-*r*
20×pow-exp add-cbrt-cube
9×pow1
8×cbrt-unprod
7×rec-exp 1-exp sqrt-prod
6×unswap-sqr
5×pow-to-exp div-inv
4×sqrt-div add-log-exp
3×associate-*r/ *-commutative
2×cbrt-undiv flip3-- pow-prod-down flip-- sqr-pow
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ un-div-inv
Counts
4 → 148
Calls
4 calls:
58.0ms
(* (pow (/ M (/ (* 2.0 d) D)) 2.0) h)
28.0ms
(* w0 (sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l)))))
8.0ms
(sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l))))
83.0ms
(* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l))

series3.0s

Counts
4 → 12
Calls
4 calls:
894.0ms
(* (pow (/ M (/ (* 2.0 d) D)) 2.0) h)
550.0ms
(* w0 (sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l)))))
721.0ms
(sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l))))
846.0ms
(* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l))

simplify3.1s

Counts
160 → 160
Iterations

Useful iterations: 2 (573.0ms)

IterNodesCost
03293086
18452743
238802382
done50002382

prune603.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.9b

localize30.0ms

Local error

Found 4 expressions with local error:

4.2b
(sqrt (- 1.0 (/ (* h (pow (/ M (/ (* 2.0 d) D)) 2.0)) l)))
4.2b
(sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l))))
5.0b
(/ (* h (pow (/ M (/ (* 2.0 d) D)) 2.0)) l)
5.0b
(* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
136×add-exp-log
63×prod-exp
46×div-exp
21×add-cbrt-cube
20×pow-exp
19×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt
13×associate-*r*
12×times-frac
8×pow1 sqrt-prod
7×rec-exp 1-exp cbrt-unprod
5×pow-to-exp
4×cbrt-undiv sqrt-div add-log-exp
3×associate-/r*
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip-- div-inv
1×frac-2neg associate-*r/ associate-*l* pow-prod-down clear-num un-div-inv *-commutative associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 115
Calls
4 calls:
19.0ms
(sqrt (- 1.0 (/ (* h (pow (/ M (/ (* 2.0 d) D)) 2.0)) l)))
5.0ms
(sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l))))
29.0ms
(/ (* h (pow (/ M (/ (* 2.0 d) D)) 2.0)) l)
72.0ms
(* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l))

series2.6s

Counts
4 → 12
Calls
4 calls:
351.0ms
(sqrt (- 1.0 (/ (* h (pow (/ M (/ (* 2.0 d) D)) 2.0)) l)))
504.0ms
(sqrt (- 1.0 (* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l))))
843.0ms
(/ (* h (pow (/ M (/ (* 2.0 d) D)) 2.0)) l)
948.0ms
(* (* (pow (/ M (/ (* 2.0 d) D)) 2.0) h) (/ 1 l))

simplify3.5s

Counts
127 → 127
Iterations

Useful iterations: done (3.5s)

IterNodesCost
02522630
16892211
235061993
done50021981

prune704.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 8.9b

regimes761.0ms

Accuracy

39.3% (2.0b remaining)

Error of 9.2b against oracle of 7.2b and baseline of 10.5b

bsearch3.0ms

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
03684
14965
done4965

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.0s9242×body80valid
622.0ms3158×body80nan